Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
quently, the number of baryons in a comoving volume of the Universe is preserved.
After the e ± pair annihilation, when the temperature drops below the electron
mass, the number of CBR photons in a comoving volume is also preserved. It is
therefore conventional to measure the universal baryon asymmetry by comparing
the number of (excess) baryons to the number of photons in a comoving volume
(post e ± annihilation). This ratio defines the baryon abundance parameter ηB:
ηB ≡ nB − nB¯ = 6.14 × 10
nγ
−10 (1.00 ± 0.04) (8.1)
The value of ηB comes from CMB anisotropies measured by WMAP [110].
In addition with such asymmetry, BBN is sensitive to the expansion rate. For
the standard model of cosmology, the Friedman equation relates the expansion
rate, quantified by the Hubble parameter H, to the matter-radiation content of
the Universe:
H 2 = 8π
(8.2)
3 GNρTOT
where GN is Newton’s gravitational constant. During the epoch we are interested
in, roughly between 50 MeV and 1 MeV, the total energy density is dominated by
radiation, i.e photons and ultra-relativistic particles, namely neutrinos, electrons
and positrons. Contrary to the baryon asymmetry of the universe, the size of the
lepton asymmetry is unknown. While some models predict a lepton asymmetry
comparable to the baryon asymmetry, it is also possible that such asymmetries
are disconnected and that the lepton asymmetry could be large enough to perturb
the standard BBN. Note that such large asymmetry would have to reside in the
neutrino sector since neutrality ensures that the electron-positron asymmetry
is comparable to the baryon asymmetry. In analogy with ηB which quantifies
the baryon asymmetry, the neutrino asymmetry, Lν = Lνe + Lνµ + Lντ may be
quantified by the neutrino chemical potentials µνα (α ≡ e, µ, τ) or equivalently
the degeneracy parameters ξνα ≡ µνα/Tν:
Lνα = nνα − nνα
nγ
= π2
12ζ(3)
Tνα
Tγ
3
ξα + ξ3 α
π 2
(8.3)
where ζ(3) ≃ 1.202. Prior to e ± annihilation, Tν = Tγ, while post-e ± annihilation
(Tνα/Tγ) = 4/11. In the rest of this chapter, since we consider neutrinos before
decoupling, we will consider equal temperatures for neutrinos and photons. 1 Since
neutrinos and anti-neutrinos should be in chemical and thermal equilibrium until
they decouple at temperature T ∼ 2 MeV, they may be well described by Fermi-
Dirac distributions with equal and opposite chemical potentials:
f(p, ξ) =
1
1 + exp(p/T + ξ)
(8.4)
1 Note that small differences in the temperature can come from out of equilibrium effects
[88] During this epoch, neutrinos are slightly coupled when electron-positron pairs annihilate
transferring their entropy to photons. This process originates non-thermal distortions on the
neutrino spectra which depend on neutrino flavour, larger for νe than for νµ or ντ.
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